VOLUME 65 : 2017

Iterative methods provide an alternative to finding the solutions of equations where analytical methods are inconvenient or even impossible to use. This study which focuses on cubic polynomial equation f (t) = at³ + bt² + ct + d = 0, a > 0 with real coefficients and having an imaginary root, found that the fixed-point iteration x_n+1 = h (x_n) where h (t) = 1/3[f (t)/f ‘(t) –b/a] will always converge to the real part x of the imaginary root of f (t) = 0 whenever b² – 3ac < 0. The only real root of g(t) = ½ f'(t) f ”(t) – af (t) = 0 was found to be the real part x of the imaginary root of f (t) = 0 and is always outside the interval formed by the critical numbers of the function f.

Keywords: complex roots, iteration, cubic polynomial, zero of a function